@article{035d84522b4746029504d1c8c0045aac, title = "Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources", abstract = "Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy capacity, i.e., the maximum rate of a secret key that can be agreed upon by the entire set of terminals, is well-understood, what remains open is the maximum rate of a secret key that can be generated when there is a restriction on the overall rate of public discussion allowed. In this work, we obtain a family of explicitly computable upper bounds on the number of bits of secret key that can be generated per bit of public discussion. These upper bounds are derived using a lamination technique based on the submodularity of the entropy function. In particular, a specific instance of these upper bounds, called the edge-partition bound, is shown to be tight for the pairwise independent network model, a special case of the hypergraphical source when the hypergraph is a graph. The secret key generation scheme achieving this upper bound is the tree-packing protocol of Nitinawarat et al., thereby resolving in the affirmative the discussion rate optimality of the tree packing protocol.", keywords = "hypergraphical sources, multiterminal source model, secrecy capacity, Secret key agreement", author = "Chung Chan and Manuj Mukherjee and Navin Kashyap and Qiaoqiao Zhou", year = "2019", month = aug, doi = "10.1109/TIT.2019.2897129", language = "English", volume = "65", pages = "5080--5093", journal = "IRE Transactions on Information Theory", issn = "0018-9448", publisher = "Institute of Electrical and Electronics Engineers", number = "8", }